Without seeing the original licence grant it's hard to be sure; the devil is in that "and/or". What you've written suggests that you may choose to use (run/distribute/modify/distribute-modified) the work under either of two licences, at your discretion.
Edit: with the clarifications you have made, this appears to me to be the case. Choose to receive the work under the LPPL, and release your modified version under that. (In the interests of free software, I urge you to receive it under the GPL, and publish your modified version under that accordingly; but that is, of course, up to you.)
If you decide to accept it under the LPPL, then I think you will be fine to redistribute your modified version under that licence, provided you meet the relevant conditions (see, eg, s.6).
If you decide to accept and use it under the GPL, you may not. GNU GPL v2 says in s.2:
But when you distribute the same sections as part of a whole which is
a work based on the Program, the distribution of the whole must be on
the terms of this License
GNU GPL v3 has a similar provision, in s.5(c):
You must license the entire work, as a whole, under this License to
anyone who comes into possession of a copy. This License will
therefore apply, along with any applicable section 7 additional terms,
to the whole of the work, and all its parts, regardless of how they